Question

Question 4: There is a system consisting of three particles where a particle can be in 0, ?, 3? and 5? energy states. Write the partition functions of the particles that meet the following conditions.

a) If the particles are distinguishable

b) Particles comply with Bose-Enistein statistics

c) If the particles match Fermi-Dirac statistics

Answer 1

Answer:

Given Data

a) If a be the one particule then the possible combination of energy are

0	3E	5E	Total energy
A	0	0	0
0	A	0	3E
0	0	A	5E

So , partition function of this particle

where

Therefore total partition function

b) For Bose Einestein statistics each particles are identical and each quantum states can contain more than one particular.

We denoted three identical particles by A . The all possible combinations of particles and quantum states are given below.

O	E	2E	Total energy
AAA	0	0	0
0	AAA	0	3E
0	0	AAA	6E
AA	A	0	E
AA	0	A	2E
0	AA	A	4E
0	A	AA	5E
A	AA	0	2E
A	0	AA	4E
A	A	A	3E

So, the partition function in this case is

c) In Fermi - Dirac statisties,the particues are spin   and indenticle.

So , the particues are obry Pauli's exclusion principle

i.e each quantum states are occupied by one particle.

Let the particles are denoted by A

So, the possible combination of quantum states and the particules are given below

0	3E	5E	Total energy
A	A	A	8E

Hence the partition function in this case is

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